A systolic algorithm is devised for solving a class of Riccati and Lyapunov equations, which makes use of a factored version of the matrix sign recursions due to Charlier and Van Dooren (MCSS 2 (1989), 109-136). The original algorithm is worked into an alternative Jacobi-type algorithm, which is readily implemented on a systolic array. Compared to the array of Charlier and Van Dooren, the present algorithm/array is conceptually simpler and, furthermore, roughly three times more efficient. (C) 1994 Academic Press, Inc.